Testing range estimators of historical volatility

This study investigates the relative performance of various historical volatility estimators that incorporate daily trading range: M. Parkinson (1980), M. Garman and M. Klass (1980), L. C. G. Rogers and S. E. Satchell (1991), and D. Yang and Q. Zhang (2000). It is found that the range estimators all perform very well when an asset price follows a continuous geometric Brownian motion. However, significant differences among various range estimators are detected if the asset return distribution involves an opening jump or a large drift. By adding microstructure noise to the Monte Carlo simulation, the finding of S. Alizadeh, M. W. Brandt, and F. X. Diebold (2002)—that range estimators are fairly robust toward microstructure effects—is confirmed. An empirical test with S&P 500 index return data shows that the variances estimated with range estimators are quite close to the daily integrated variance. The empirical results support the use of range estimators for actual market data. © 2006 Wiley Periodicals, Inc. Jrl Fut Mark 26:297–313, 2006     

Pricing real options under the constant elasticity of variance diffusion

Much of the work on real options assumes that the underlying state variable follows a geometric Brownian motion with constant volatility. This paper uses a more general assumption for the state variable process that better captures the empirical regularities found in commodity markets. We use the constant elasticity of variance diffusion, where volatility is a function of underlying asset prices, and we provide analytic solutions for perpetual American options. We show that a firm that uses the standard lognormal assumption is exposed to significant errors of analysis, which may lead to nonoptimal investment and disinvestment decisions. © 2010 Wiley Periodicals, Inc. Jrl Fut Mark 31:230–250, 2011     

Arbitrage with Fractional Brownian Motion

Fractional Brownian motion has been suggested as a model for the movement of log share prices which would allow long–range dependence between returns on different days. While this is true, it also allows arbitrage opportunities, which we demonstrate both indirectly and by constructing such an arbitrage. Nonetheless, it is possible by looking at a process similar to the fractional Brownian motion to model long–range dependence of returns while avoiding arbitrage.     

THE EFFECT OF ESTIMATION IN HIGH‐DIMENSIONAL PORTFOLIOS

We study the effect of estimated model parameters in investment strategies on expected log‐utility of terminal wealth. The market consists of a riskless bond and a potentially vast number of risky stocks modeled as geometric Brownian motions. The well‐known optimal Merton strategy depends on unknown parameters and thus cannot be used in practice. We consider the expected utility of several estimated strategies when the number of risky assets gets large. We suggest strategies which are less affected by estimation errors and demonstrate their performance in a real data example. Strategies in which the investment proportions satisfy an L₁ ‐constraint are less affected by estimation effects.     

SOLUTION OF THE EXTENDED CIR TERM STRUCTURE AND BOND OPTION VALUATION

The extended Cox-Ingersoll-Ross (ECIR) models of interest rates allow for time-dependent parameters in the CIR square-root model. This article presents closed-form pathwise unique solutions of these unsolved stochastic differential equations (s.d.e.s) in terms of functionals of their driving Brownian motion and parameters. It is shown that quadratics in solution of linear s.d.e.s solve the ECIR model if and only if the dimension of the model is a positive integer and that this solution can be achieved by construction of a pathwise unique generalized Ornstein-Uhlenbeck process from the ECIR Brownian motion. For real valued dimensions an extension of the time-change theorem of Dubins and Schwarz (1965) is presented and applied to show that a lognormal process solves the model through a stochastic time change. Pathwise equivalence to a rescaled time-changed Bessel square process is also established. These novel results are applied to characterize zero-hitting time and to produce transition density and zero-hitting conditions for the ECIR spot rate. the CIR term structure is then extended to ECIR under no arbitrage, and its solutions and the transition density are represented under a new ECIR martingale measure. the findings are employed to derive a closed-form ECIR bond option valuation formula which generalizes that obtained by CIR (1985).     

Asking “What Else?” to identify unintended negative consequences

With the advent of big data, the Internet of Things, cognitive computing, and social media, it is becoming more difficult to argue that one could not have known or at least have considered more alternatives, particularly negative unintended consequences that happen in addition to the intended positive ones. Organizations too often make a decision that will produce a positive consequence and then focus on how to implement it, rarely stepping back to ask “What else could happen?” Any decision changes the system in which it exists. The longer the time required to implement a decision, the more systemic changes can alter the effects of the decision on the system. Decisions to implement Corporate Social Responsibility and sustainability initiatives usually involve many different stakeholders and may involve systems in which organizations have little expertise or experience. A major negative unintended consequence, even for a CSR initiative, can damage the stakeholders’ trust in the organization. This article proposes a 5-step process to answer the question “What else could happen?” in order to identify possible unintended negative consequences, thereby helping organizations support their commitment to people, planet, and profit.     

VALUATION OF CLAIMS ON NONTRADED ASSETS USING UTILITY MAXIMIZATION

A topical problem is how to price and hedge claims on nontraded assets. A natural approach is to use for hedging purposes another similar asset or index which is traded. To model this situation, we introduce a second nontraded log Brownian asset into the well-known Merton investment model with power law and exponential utilities. The investor has an option on units of the nontraded asset and the question is how to price and hedge this random payoff. The presence of the second Brownian motion means that we are in the situation of incomplete markets. Employing utility maximization and duality methods we obtain a series approximation to the optimal hedge and reservation price using the power utility. The problem is simpler for the exponential utility, and in this case we derive an explicit representation for the price. Price and hedging strategy are computed for some example options and the results for the utilities are compared.     

Bond returns and betas as dependent upon conditioned Brownian motion

This research uses a conditioned Brownian motion process, the Brownian bridge, to analyze bond return dynamics and systematic risk. The results are contrasted with prior results that assume that yields follow unconditioned Brownian motion and reveal significant differences. Expected returns and the variance of expected returns can be given in much more concise terms that are more easily interpreted. Also, bond betas are demonstrated to depend on returns above an initially stated deterministic yield and shown to fluctuate proportionately with this excess return, which can often be negative. Finally, empirical tests show that bond excess returns do follow a Brownian bridge process or at least do so up to a multiple of the conditioned drift term.     

外国直接投资、出口倾向与技术溢出效应

本文利用2001、2002、2003年的行业数据,对比研究了在外商投资企业出口倾向较高的行业和出口倾向较低的行业,外商投资企业对我国内资企业的技术溢出效应。结果表明,在外商投资企业出口倾向较高的行业,外商投资企业通过竞争效应、研发效应和模仿效应对我国内资企业产生较明显的技术溢出效应,在外商投资企业出口倾向较低的行业,其技术溢出效应不明显。     

E-commerce and the retail process: a review

Views abound on the impact of the Internet and e-commerce on traditional forms of retailing. Scenarios range from on the one hand, the almost total devastation of existing physical retailing to, on the other, limited if any impact upon “real” retailing.Despite excessive hype, spectacular failures and the myriad of conflicting views and crystal-ball gazing, e-commerce processes and procedures provide the potential for a fundamental reassessment of how retailing operates and how retailers behave. Without doubt, the existing ways of operating and the associated cost structures within retailing will be reassessed under the onslaught of new technology and new retail structures.This paper reviews the published evidence on the impact of e-commerce on the retail process. It reviews the situation rather than introducing new evidence. The focus is on the process as it supports B2C activity and how retail processes and procedures could be affected by e-commerce, rather than a pre-occupation with sales impact through traditional merchandise and product sector typologies.Three conclusions are drawn. First, the largest retailers are now pursuing Internet-enabled advantages and cost reductions in operations, which could translate to an enhanced competitive position in process, structure and relationship terms. Secondly, consumer reactions to the new real and virtual offers will be fundamental to their success and failure, but as yet consumer reactions are not fully understood. Thirdly, existing retail floorspace will need enhancement in quality and presentation if it is to continue to provide retail functions.     

A Simple Way to Reduce Estimation Bias in Some Dynamic Choice Models

This study proposes a simple estimator for dynamic choice models with continuous unobserved heterogeneity, state dependence induced by a first-order Markov process, and lagged choice coefficients that are not brand specific. As opposed to the estimator most frequently used in marketing studies, which drops the first choice of each panelist, this estimator keeps that choice in the estimation sample but ignores the impact of presample choices on first observed choice. The proposed method presents major advantages over dropping the first observation: (1) it yields low bias estimates for state dependence coefficients and, thus, it can be used to assess the presence and the magnitude of state dependence; (2) it is informative about the magnitude of bias in its estimates; and (3) it yields substantially and significantly smaller biases. The results of this study can be used to determine if the proposed method is suitable for specific applications on real data.     

贸易自由化对中国城镇劳动力市场性别歧视的影响

贸易自由化既可缩小也可扩大性别工资差。绝大多数实证研究,例如Oosdendorp(2004),都采用的是较宏观的行业加总数据,并着重于职业性别工资差。然而,行业加总的职业工资不能控制教育水平和经验变量,因此很难判断性别工资差的变化到底来自个人特征因素还是贸易自由化。文章运用中国城镇居民家庭的微观数据,运用difference-in-difference的方法,在消除了不随时间改变的固定效应和随时间变化的系统冲击的基础上,检验了1988年到1995年中国第一次贸易自由化兴起时期,贸易开放度的变化对不同教育水平的性别工资差的影响。结果显示,这一时期贸易开放度和性别工资差之间的相互关系主要来源于进口开放度的变化:随着进口开放度的上升,低教育人群的性别工资差显著扩大,而高教育人群的性别工资差却呈现相反趋势。出口开放度的上升对低教育人群的性别工资差没有显著影响,但与进口开放度的上升一样,它缩小了高教育人群的性别工资差。     

欧洲经济发展问题浅析

随着欧洲主权债务危机的越演越烈,人们一直在探讨债务危机发生的原因,但很少从深层次的角度分析欧洲经济发生危机最根本的原因。欧洲在过去的几十年里,经济发展一直仅次于美国,但近些年的发展明显滞后于美国,本文从欧洲的经济制度、政策模式、技术创新等方面分析了经济发展缓慢的原因及未来的几年内欧洲面临的挑战。     

基于中国实时数据的产出缺口估计及其修正——兼论中国产出缺口和通货膨胀之间的预测关系

基于1994Q1-2008Q4的数据并分别利用三次趋势和HP滤波两种模型方法估计中国的实时、准实时和最终产出缺口,分析显示,这一时期中国的产出缺口遭受了较大而且高度持续的修正,说明中国的实时产出缺口和基于事后修正数据估计的产出缺口有很大不同。进一步比较实时产出缺口和最终产出缺口与通货膨胀之间的菲利普斯曲线预测关系,发现实时产出缺口的通胀预测表现显著好于最终产出缺口。由于货币政策决策总发生在"实时",不能等待事后产出缺口等数据信息的修正,因此,区分实时数据和事后修正数据对经济分析和政策决策而言可能就十分重要。     

Pricing Options With Curved Boundaries1

This paper provides a general valuation method for the European options whose payoff is restricted by curved boundaries contractually set on the underlying asset price process when it follows the geometric Brownian motion. Our result is based on the generalization of the Levy formula on the Brownian motion by T. W. Anderson in sequential analysis. We give the explicit probability formula that the geometric Brownian motion reaches in an interval at the maturity date without hitting either the lower or the upper curved boundaries. Although the general pricing formulae for options with boundaries are expressed as infinite series in the general case, our numerical study suggests that the convergence of the series is rapid. Our results include the formulae for options with a lower boundary by Merton (1973), for path-dependent options by Goldman, Sossin, and Gatto (1979), and for some corporate securities as special cases.     

BUY‐LOW AND SELL‐HIGH INVESTMENT STRATEGIES

Buy‐low and sell‐high investment strategies are a recurrent theme in the considerations of many investors. In this paper, we consider an investor who aims at maximizing the expected discounted cash‐flow that can be generated by sequentially buying and selling one share of a given asset at fixed transaction costs. We model the underlying asset price by means of a general one‐dimensional Itô diffusion X , we solve the resulting stochastic control problem in a closed analytic form, and we completely characterize the optimal strategy. In particular, we show that, if 0 is a natural boundary point of X , e.g., if X is a geometric Brownian motion, then it is never optimal to sequentially buy and sell. On the other hand, we prove that, if 0 is an entrance point of X , e.g., if X is a mean‐reverting constant elasticity of variance (CEV) process, then it may be optimal to sequentially buy and sell, depending on the problem data.     

Economic analysis of injury prevention--applying results and methodologies from cost-of-injury studies

Injuries pose an economic problem of immense proportion to communities in every society. The economic burden from injuries can be quantified through cost-of-injury studies, using techniques adopted from cost-of-illness research. This study explores the feasibility of applying results and methodologies from existing cost-of-injury studies in economic analyses of injury prevention interventions and programmes. The literature on cost-of-injury studies and economic appraisals of injury prevention efforts was examined to elicit studies that calculated injury costs. Studies were accepted for inclusion if they included an analysis of the costs of all injuries occurring in a geographical area (community, region or country) during a specific time period, employed a societal perspective and an incidence-based costing approach and were conducted in industrialized countries. There were 12 studies that met the inclusion criteria. The average total cost per injury case was USD $3536, while the average share of indirect to total cost per injury case was 71%. However, the cost figures showed wide variation across the studies. Based on the limited similarity of findings from the studies, it was concluded that it is not feasible to apply results and methodologies from existing cost-of-injury studies. The cost estimators described in this study could possibly be adapted for use as reference points in economic analyses of existing programmes, but any other uses should be approached with caution. Locally obtained data are needed for reliable economic analyses of injury prevention interventions and programmes.     

The characteristic function of rough Heston models

It has been recently shown that rough volatility models, where the volatility is driven by a fractional Brownian motion with small Hurst parameter, provide very relevant dynamics in order to reproduce the behavior of both historical and implied volatilities. However, due to the non‐Markovian nature of the fractional Brownian motion, they raise new issues when it comes to derivatives pricing. Using an original link between nearly unstable Hawkes processes and fractional volatility models, we compute the characteristic function of the log‐price in rough Heston models. In the classical Heston model, the characteristic function is expressed in terms of the solution of a Riccati equation. Here, we show that rough Heston models exhibit quite a similar structure, the Riccati equation being replaced by a fractional Riccati equation.     

VASIČEK BEYOND THE NORMAL

A general Ornstein-Uhlenbeck (OU) process is obtained upon replacing the Brownian motion appearing in the defining stochastic differential equation with a general Lévy process. Certain properties of the Brownian ancestor are distribution-free and carry over to the general OU process. Explicit expressions are obtainable for expected values of a number of functionals of interest also in the general case. Special attention is paid here to gamma- and Poisson-driven OU processes. The Brownian, Poisson, and gamma versions of the OU process are compared in various respects; in particular, their aptitude to describe stochastic interest rates is discussed in view of some standard issues in financial and actuarial mathematics: prices of zero-coupon bonds, moments of present values, and probability distributions of present values of perpetuities. The problem of possible negative interest rates finds its resolution in the general setup by taking the driving Lévy process to be nondecreasing.     

Economic analysis of injury prevention – applying results and methodologies from cost-of-injury studies

Injuries pose an economic problem of immense proportion to communities in every society. The economic burden from injuries can be quantified through cost-of-injury studies, using techniques adopted from cost-of-illness research. This study explores the feasibility of applying results and methodologies from existing cost-of-injury studies in economic analyses of injury prevention interventions and programmes.

The literature on cost-of-injury studies and economic appraisals of injury prevention efforts was examined to elicit studies that calculated injury costs. Studies were accepted for inclusion if they included an analysis of the costs of all injuries occurring in a geographical area (community, region or country) during a specific time period, employed a societal perspective and an incidence-based costing approach and were conducted in industrialized countries. There were 12 studies that met the inclusion criteria.

The average total cost per injury case was US$3536, while the average share of indirect to total cost per injury case was 71%. However, the cost figures showed wide variation across the studies. Based on the limited similarity of findings from the studies, it was concluded that it is not feasible to apply results and methodologies from existing cost-of-injury studies. The cost estimators described in this study could possibly be adapted for use as reference points in economic analyses of existing programmes, but any other uses should be approached with caution. Locally obtained data are needed for reliable economic analyses of injury prevention interventions and programmes.